Mumbai has refineries (though technically in nearby areas like Trombay), Cochin has the Kochi Refinery, and Chennai has the Chennai Refinery (Manali). Tuticorin (Thoothukudi) is a major port but does not have a significant oil refinery - it primarily handles cargo, coal, and container operations. Therefore, Tuticorin is the correct answer as the port without an oil refinery.